Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p -Laplacian Operator

Jinhua Wang and Hongjun Xiang

Abstract and Applied Analysis, 2010, vol. 2010, 1-12

Abstract:

The upper and lower solutions method is used to study the p -Laplacian fractional boundary value problem D 0 + γ ( ϕ p ( D 0 + α u ( t ) ) ) = f ( t , u ( t ) ) , 0 < t < 1 , u ( 0 ) = 0 , u ( 1 ) = a u ( ξ ) , D 0 + α u ( 0 ) = 0 , and D 0 + α u ( 1 ) = b D 0 + α u ( η ) , where 1 < α , γ ⩽ 2 , 0 ⩽ a , b ⩽ 1 , 0 < ξ , η < 1 . Some new results on the existence of at least one positive solution are obtained. It is valuable to point out that the nonlinearity f can be singular at t = 0,1 or u = 0 .

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:971824

DOI: 10.1155/2010/971824

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